Floating-point vs Fixed-point representation

In fixed-point representation, the position of the decimal (or binary) point is fixed and predetermined, meaning there's a fixed number of digits before and after the point, while in floating-point representation, the decimal point's position can "float" relative to the significant digits, similar to scientific notation (e.g., F x 10^E). 

Key Differences:

• Decimal Point Placement:

  • Fixed-point: The decimal point's location is static; for example, a fixed-point number might always have 2 digits after the decimal point. 
  • Floating-point: The decimal point's position is dynamic and determined by an exponent, allowing for a wide range of values, from very small to very large, by shifting the decimal point relative to the significant digits. 

• Precision:

  • Fixed-point: Offers exact precision for values within its defined range, making it ideal for financial and accounting applications where absolute accuracy is crucial. 
  • Floating-point: Provides approximate precision and can introduce rounding errors, but it's suitable for scientific and general-purpose calculations where a wide dynamic range is needed. 

• Applications:

  • Fixed-point: Commonly used in embedded systems, digital signal processing, and control systems where computational efficiency and predictability are critical. 
  • Floating-point: Used in scientific computing, graphics, and any application requiring a broad range of magnitudes.